How to make an animation node particle wiggle?
Start by getting the particles from an object, each item from that list is an individual particle which you can get the location of by connecting to a particle info node. Then you mix a vector wiggle to the particle location and use that to set the location of an object.

Here I take the original particle z location and mix a wiggle into the x and y location to place an object that follows the particle downwards.



Add that into a loop to repeat for each particle.